Counting free subgroups of finite index
Copyright policy )Counting free subgroups of finite index
Let \(G\) be a finitely generated (infinite) virtually free group and denote by \(m_ G\) the least common multiple of the orders of the finite subgroups in \(G\). The author continues the investigation of the function \(b_ G : N \to N\), where \(b_ G (\lambda)\) is the number of free subgroups of index \(\lambda m_ G\) in \(G\). An asymptotic expansion of the function \(b_ G(\lambda)\) is found. Also the author considers examples which demonstrate the precision of the expansions obtained.
- Bielefeld University Germany
Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations, Generators, relations, and presentations of groups, Topological methods in group theory, orders of finite subgroups, number of free subgroups, Free nonabelian groups, Subgroup theorems; subgroup growth, Fundamental groups and their automorphisms (group-theoretic aspects), Groups acting on trees, Asymptotic results on counting functions for algebraic and topological structures, finitely generated virtually free groups
Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations, Generators, relations, and presentations of groups, Topological methods in group theory, orders of finite subgroups, number of free subgroups, Free nonabelian groups, Subgroup theorems; subgroup growth, Fundamental groups and their automorphisms (group-theoretic aspects), Groups acting on trees, Asymptotic results on counting functions for algebraic and topological structures, finitely generated virtually free groups
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